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# If AB = 5cm, is the perimeter △ABC > 20cm? (1) BC = 13cm (2) 10cm < A

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Re: If AB = 5cm, is the perimeter ABC > 20cm? (1) BC = 13cm (2) 10cm < A [#permalink]
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Bunuel wrote:
If AB = 5cm, is the perimeter △ABC > 20cm?

(1) BC = 13cm
(2) 10cm < AC < 13cm

In any triangle, (difference of other two sides) < Third side < (sum of other two sides)

And, (BC-AB) < AC < (BC + AB)

⇒ 8 < AC < 18.

Adding (AB + BC) in all the sides of the inequality;

⇒ 8 + (AB + BC) < (AB + BC +AC) < 18 + (AB + BC)

⇒ 8 + 5 + 13 < Perimeter < 18 + 5 + 13

⇒ 26 < Perimeter < 36.

Hence, the perimeter of triangle ABC > 20;SUFFICIENT.

(2) 10 < AC < 13

AB = 5.

Suppose, AC = 10.

Then, AC –AB < BC < AC + AB

⇒ 5 < BC < 15.

⇒ Still, perimeter will lie in the range; 20 < Perimeter < 30.

⇒ But, AC is itself greater than 10, So Overall perimeter will always be more than 20;SUFFICIENT.